On one-way functions by Anshel and Goldfeld

One-way functions play fundamental role in public-key cryptography. In this paper, one-way functions proposed by Anshel and Goldfeld in 1997 are reformulated, and their computational complexity and applications are discussed. Their one-way functions are constructed using L-functions associated with elliptic curves defined over the rational number field. Their functions are unique and also have potential applications in post-quantum cryptography.